Using the Failure Assessment Diagram Method with Fatigue ... · • Determine the initial FAD Point...
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Using the Failure Assessment Diagram Method with Fatigue Crack Growth to Determine Leak-Before-Rupture Presented By: Chris Tipple SIMULIA Community Conference May 2012
Transcript of Using the Failure Assessment Diagram Method with Fatigue ... · • Determine the initial FAD Point...
Using the Failure Assessment Diagram Method with Fatigue Crack Growth to
Determine Leak-Before-Rupture
Presented By: Chris Tipple SIMULIA Community Conference
May 2012
Outline
• Determine the initial FAD Point for a crack – Elastic and plastic J results – Discover the geometry factor “F” – Calculate the FAD Curve – Calculate the FAD Point (Lr, Kr)
• Determine crack growth
– Paris equation – Iterate the FAD procedure for each crack dimension
Motivation
• What advantage is there to performing an elastic/plastic crack assessment rather than linear elastic fracture mechanics?
0.0
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0.4
0.6
0.8
1.0
1.2
0 0.2 0.4 0.6 0.8 1 1.2 1.4Kr =
K e
last
ic/K
tot
al =
K/t
ough
ness
Lr = reference stress/yield strength
Default FAD vs. Material Specific FAD
Computed FAD curve Default FAD curve
Default FAD
Material & GeometrySpecific FAD
– Material and geometry specific FAD curve
– Includes the “tearing” effect of ductility in addition to brittle fracture
Highly Stressed Location Magnitude of Maximum Principal Stress (Normalized)
Direction of Maximum Principal Stress (Vessel Hoop)
Crack Inserted Inserted Crack Mesh (Tied Contact)
Magnitude of Maximum Principal Stress with Inserted Crack
Un-Cracked Mesh vs. Cracked Mesh Magnitude of Maximum Principal Stress
Magnitude of Maximum Principal Stress with Inserted Crack
Failure Assessment Diagram (FAD)
Acceptable flaws
Unacceptable flaws
Lr max
Brittle Fracture
Plastic Collapse
Fracture + Plastic Deformation
Critical flaw
The Geometry Factor • Evaluate material specific equation at Lr=1
• Find the nominal load at the intersection with the “total J/elastic J” curve • The geometry factor F is given by:
• Compute the reference stress at each load increment, σi , using the geometry factor F
+++=
= YSYSLrelastic
total EEJJ
σσ002.015.0002.01
1
1nominal =
=Lr
YSFσ
σ
Firef σσ =
Elastic vs. Total J-Integral (Continued)
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2500.0
0 200 400 600 800 1000 1200
J-in
tegr
al (p
si-in
)
Load, internal pressure (psi)
Elastic-Plastic J-integral Results, Infer Elastic J
Total J Computed elastic J
J_Total
Infer Elastic J
Elastic J integral shown with red dashed line Total J integral shown with blue solid line Interested in the ratio of the two
Elastic vs. Total J Integral
y = 0.00039x2
R² = 1.00000
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0 50 100 150 200 250 300
J-in
tegr
al (p
si-in
)
Load, internal pressure (psi)
J-integral elastic range for curve-fit
Total J Computed elastic J
Compare curve-fit Poly. (Total J)
Data Points: Elastic/Plastic J Integral Red Dashed Line: Computed Elastic J-Integral Blue Solid Line: Elastic Curve Fit
Steps to the Geometry Factor F
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0 200 400 600 800 1000 1200
J tot
al/J
ela
stic
Load, internal pressure (psi)
J Total to J Elastic Ratio, Nominal Load at Lr=1
J_total/J_elastic J/Jel at Lr=1 Nominal load at Lr=1
Nominal Load = 934.35 psi
MaterialSpecific Value = 2.53
J_Total / J_Elastic
YS
YSLrelastic
total
EE
JJ
σσ 002.01
5.0002.011 +
++==
Find the Material Specific value From the intersection of the material specific value and the J-ratio, find the nominal load
97.461nominal
===Lr
YSFσ
σ
Firef σσ =
FAD Curve • Compute the analysis specific FAD curve Lr values using the reference
stress at each load increment
• Compute the analysis specific FAD curve Kr values using the “J_elastic /J_total” ratio at each load increment
YS
refLrσσ
=
total
elastic
JJKr =
FAD Evaluation Point • Compute the crack FAD evaluation point at the given load (design load or
operating load)
• Compute Lr using the reference stress at the given evaluation load
• Compute Kr using the stress intensity K from the elastic analysis and the material toughness, Kmat
YS
refLrσσ
=
matKKKr =
FAD Evaluation Point
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0.4
0.6
0.8
1.0
1.2
0 0.2 0.4 0.6 0.8 1 1.2 1.4Kr =
K e
last
ic/K
tota
l = K
/tou
ghne
ss
Lr = reference stress/yield strength
Computed FAD Curve and Evaluation Point
Computed FAD curve Default FAD curve
Corner Crack Evaluation Point
Default FADCurve
Material & GeometrySpecific FAD Curve
Lr Max
Corner CrackEvaluation Point
Outline
• Determine the initial FAD Point for a crack – Elastic and plastic J results – Discover the geometry factor “F” – Calculate the FAD Curve – Calculate the FAD Point (Lr, Kr)
• Determine crack growth
– Paris equation – Iterate the FAD procedure for each crack dimension
Crack Dimension Convention
a
c• a = crack depth (along axis of manway) • c = crack length (along axis of vessel)
Crack Growth
mKCdNda )(∆=
a = 0.50 in c = 0.50 in
0 Cycles
a = 0.75 in c = 1.07 in
27,659 Cycles
a = 1.00 in c = 1.60 in
51,422Cycles
• Two Equations – da/dN and dc/dN
• Three Unknowns – a, c and N
• Define initial crack depth (a0) and incremental crack depth change (Δa)
Crack Dimensional Growth
(A)
(B)
(C)
0
0.5
1
1.5
0 10000 20000 30000 40000 50000 60000
Crac
k D
epth
a, i
n
Cycles
Crack Depth with Number of Cycles
Crack Depth a, in 80% Thickness
Number of cycles @ 80% Thickness Poly. (Crack Depth a, in)
Crack Depth / Total Thickness = 80% = 0.95 in
46,279Cycles(A)
(B)
(C)
0
0.5
1
1.5
2
0 10000 20000 30000 40000 50000 60000
Crac
k Le
ngth
c, i
n
Cycles
Crack Length with Number of Cycles
Crack Depth a, in Crack Length @ 80% ThicknessNumber of Cycles @ 80% Thickness Poly. (Crack Depth a, in)
Crack Length at 80% Crack Depth = 1.49 in
46,279Cycles(A)
(B)
(C)
Re-characterization
)( sst atcc −+=
t
ct
cs
as
• The 80% through-thickness crack can be re-characterized as a through-wall crack of length c = 1.73 in –
– Re-evaluate the FAD point for the through-wall crack
(t-as)
FAD Evaluation Point
• Crack satisfies leak-before-rupture condition
46,279 Cycles
Conclusions
• Determined the FAD Point for the initial corner crack in the manway
• Fatigue analysis determined crack dimensions at 80% depth
• Re-characterized to through-wall crack and used to determine leak before rupture
• Contact Information Chris Tipple Quest Integrity Group, LLC Phone: (303) 938-3020 E-Mail: [email protected]
